




Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
25.1 Derivatives of Inverse Sine and Cosine. Applying the inverse rule (25.1) with f (x) = sin(x) yields d dxhsin°1(x)i = 1 cos°sin°1(x)¢.
Typology: Lecture notes
1 / 8
This page cannot be seen from the preview
Don't miss anything!
d
dx
h sin
° 1 (x)
i (^) d
dx
h tan
° 1 (x)
i (^) d
dx
h sec
° 1 (x)
i
d
dx
h cos
° 1 (x)
i (^) d
dx
h cot
° 1 (x)
i (^) d
dx
h csc
° 1 (x)
i
d
dx
h f
° 1 (x)
f 0
f °^1 (x)
d
dx
h sin
° 1 (x)
cos
sin
° 1 (x)
cos
sin
° 1 (x)
sin°^1 (x) =
the angle ° º 2 ∑ μ ∑ º 2
for which sin( μ ) = x
° 1
º
º
sin
° 1 (x)
p
sin
° 1 (x)
p 1 ° x^2
1
sin°^1 (x)
x
| {z }
cos
sin°^1 (x)
d
dx
h sin
° 1 (x)
p 1 ° x^2
x
y
1
° º 2
º 2 f^ (x)^ =^ sin
° 1 (x)
f
0 (x) =
p 1 ° x^2
f (x) = cos°^1 (x)
° 1
sin
° 1
° 1
d
dx
h cos°^1 (x)
p 1 ° x^2
x
f (x) = cos°^1 (x)^ º
f
0 (x) =
p 1 ° x^2
d
dx
h sec
° 1 (x)
f 0
f °^1 (x)
sec
f °^1 (x)
· tan
f °^1 (x)
sec
sec°^1 (x)
· tan
sec°^1 (x)
sec
° 1 (x)
d
dx
h sec
° 1 (x)
x · tan
sec°^1 (x)
sec
° 1 (x)
( (^) p
p
d
dx
h sec
° 1 (x)
x
p x^2 ° 1
°x
p x^2 ° 1
d
dx
h sec
° 1 (x)
|x|
p x^2 ° 1
y = f
0 (x) =
|x|
p x^2 ° 1
y
º
º 2 y^ =^ f^ (x)^ =^ sec
° (^1) (x)
° 1 1
d
dx
h csc°^1 (x)
|x|
p x^2 ° 1
d
dx
h csc°^1
g(x)
Øg(x)
q
(g(x))
g^0 (x) =
°g^0 (x) Ø Øg(x)
q
(g(x))
d
dx
h sin
° 1 (x)
p 1 ° x^2
d
dx
h sin
g(x)
q
1 ° (g(x))
2
g
0 (x)
d
dx
h cos
° 1 (x)
p 1 ° x^2
d
dx
h cos
g(x)
q
1 ° (g(x))
2
g
0 (x)
d
dx
h tan°^1 (x)
1 + x^2
d
dx
h tan°^1
g(x)
1 + (g(x))
2
g^0 (x)
d
dx
h cot°^1 (x)
1 + x^2
d
dx
h cot°^1
g(x)
1 + (g(x))
2
g^0 (x)
d
dx
h sec°^1 (x)
|x|
p x^2 ° 1
d
dx
h sec°^1
g(x)
g
0 (x) Ø Øg(x)
q
(g(x))
d
dx
h csc
° 1 (x)
|x|
p x^2 ° 1
d
dx
h csc
g(x)
°g^0 (x) Ø Øg(x)
q
(g(x))^2 ° 1
d
dx
hp cos°^1 (x)
d
dx
h° cos
° 1 (x)
2
cos
° 1 (x)
2 d dx
h cos
° 1 (x)
i
cos
° 1 (x)
(^2) p°^1
1 ° x^2
p cos°^1 (x)
p 1 ° x^2
d
dx
h e
tan°^1 (x)
i = e
tan°^1 (x) d dx
h tan
° 1 (x)
i = e
tan°^1 (x) 1 1 +x^2
etan
° (^1) (x)
1 +x^2
d
dx
h tan°^1
ex
1 + (^) (ex)^2
d
dx
h ex
1 + e^2 x^
ex^ =
e
x
1 + e^2 x^
d
dx
c f (x)
= c f 0 (x)
d
dx
f (x) ± g(x)
= f 0 (x) ± g^0 (x)
d
dx
f (x)g(x)
= f 0 (x)g(x) + f (x)g^0 (x)
d
dx
f (x)
g(x)
f 0 (x)g(x) ° f (x)g^0 (x)
(g(x))^2
d
dx
f
g(x)
= f
0 (g(x)) g
0 (x)
d
dx
f
° 1 (x)
f 0
f °^1 (x)
d
dx
h cos°^1 (x)
p 1 ° x^2
d
dx
h csc
° 1 (x)
|x|
p x^2 ° 1
d
dx
h cot
° 1 (x)
1 + x^2
° 1 °p 2 x
tan°^1 (x)
x tan
° 1 (x)
º x
º x
sin
° 1 (x)
º x
x^5
tan°^1 ( º x)
ln(x)
x sin(x)
ln(x)
d
dx
h cos
° 1 (x)
p 1 ° x^2
d
dx
h cos
° 1 (x)
° sin
cos°^1 (x)
cos°^1 (x) º (^) 0
1
cos°^1 (x)
OPP HYP
p 1 °x^2 1 =^
p
d
dx
h cos
° 1 (x)
p 1 ° x^2
x
d
dx
h cot°^1 (x)
1 + x^2
d
dx
h ln
tan°^1 (x)
tan°^1 (x)
d
dx
h tan°^1 (x)
tan°^1 (x)
1 + x^2
tan°^1 (x)
1 + x^2
d
dx
h tan
º x
º
1 + ( º x)^2
º
1 + º^2 x^2
d
dx
h ln
sin°^1 (x)
sin
° 1 (x)
d
dx
h sin°^1 (x)
sin
° 1 (x)
p 1 °x^2
sin
° 1 (x)
p 1 °x^2
d
dx
h sec
x
Øx^5
q ° x^5
5 x
5 x
4 Ø Øx^5
p x^10 ° 1
Øx
p x^10 ° 1
d
dx
h tan
ln(x)
ln(x)
x
x + x
ln(x)
d
dx
h x sin
ln(x)
¢i = 1 · sin
ln(x)
d
dx
h sin
ln(x)
¢i
= sin
ln(x)
q 1 °
ln(x)
x
= sin
ln(x)
q 1 °
ln(x)